trigonometry: (A2) Compound angles question

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dxnixl
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Hi,

Could someone help me out with what this questions asking me exactly?
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RDKGames
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(Original post by dxnixl)
Hi,

Could someone help me out with what this questions asking me exactly?

Thanks
It is asking you to find the value of \alpha such that \dfrac{1+\tan x}{1-\tan x} \equiv \tan(x+\alpha)
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dxnixl
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(Original post by RDKGames)
It is asking you to find the value of \alpha such that \dfrac{1+\tan x}{1-\tan x} \equiv \tan(x+\alpha)
oH! thankyou

so i’m assuming x and  \alpha are two different variables?

sorry if i’m a bit slow we just went over this today ergh
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RDKGames
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(Original post by dxnixl)
oH! thankyou

so i’m assuming x and  \alpha are two different variables?

sorry if i’m a bit slow we just went over this today ergh
x is the variable.

Alpha is a constant value.
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dxnixl
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(Original post by RDKGames)
x is the variable.

Alpha is a constant value.
so is the answer 45 because x and alpha must be the same so that alphas eliminated on the RHS?

or am i just lost :’)
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DFranklin
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(Original post by dxnixl)
so is the answer 45 because x and alpha must be the same so that alphas eliminated on the RHS?

or am i just lost :’)
If "x and alpha must be the same", then surely x = alpha? I don't think that's what you actually meant to say...
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Nick_2440
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(Original post by dxnixl)
Hi,

Could someone help me out with what this questions asking me exactly?
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Starting with: tan(x + a) = (tan a + tan x) / (1 - tan a tan x)
Notice that if tan a = 1, then the expression becomes identical to what is in the question: (1 + tan x) / (1 - tan x)
So let a = arctan(1) = pi/4 to get tan(x + pi/4).

Edit: or tan(x + 45) if working in degrees instead of radians.

Hope this helps
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dxnixl
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(Original post by Nick_2440)
Starting with: tan(x + a) = (tan a + tan x) / (1 - tan a tan x)
Notice that if tan a = 1, then the expression becomes identical to what is in the question: (1 + tan x) / (1 - tan x)
So let a = arctan(1) = pi/4 to get tan(x + pi/4).

Hope this helps
OH RIGHT yeah i got it now ergh thanks 🤦*♂️
because tan(alpha) has to equal 1 to get the 1 in the numerator and so alpha can only be 45 degrees
thanks
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